MATLAB Mathematics - SERC - Index of

Initial Value Problems for ODEs and DAEs
The equations for the bouncing ball are
y′ 1 = y 2
y′ 2 = – 9.8
In this example, the event function is coded in a subfunction events
[value,isterminal,direction] = events(t,y)
which returns
• A value of the event function
• The information whether or not the integration should stop when value = 0
(isterminal = 1 or 0, respectively)
• The desired directionality of the zero crossings:
-1 Detect zero crossings in the negative direction only
0 Detect all zero crossings
1 Detect zero crossings in the positive direction only
The length of value, isterminal, and direction is the same as the number of
event functions. The ith element of each vector, corresponds to the ith event
function. For an example of more advanced event location, see orbitode
(“Example: Advanced Event Location” on page 5-32).
In ballode, setting the Events property to @events causes the solver to stop the
integration (isterminal = 1) when the ball hits the ground (the height y(1) is
0) during its fall (direction = -1). The example then restarts the integration
with initial conditions corresponding to a ball that bounced.
To run this example, click on the example name, or type ballode at the
command line.
function ballode
%BALLODE Run a demo of a bouncing ball.
tstart = 0;
tfinal = 30;
y0 = [0; 20];
5-29